Approximation Theory and Harmonic Analysis on Spheres and Balls

• Main Authors: Dai, Feng. (Author), Xu, Yuan. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Global analysis (Mathematics).; Fourier analysis.; Functions, special.; Analysis.; Approximations and Expansions.; Fourier Analysis.; Special Functions.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4614-6660-4

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with...

Table of Contents:

• 1 Spherical Harmonics
• 2 Convolution and Spherical Harmonic Expansion
• 3 Littlewood-Paley Theory and Multiplier Theorem
• 4 Approximation on the Sphere
• 5 Weighted Polynomial Inequalities
• 6 Cubature Formulas on Spheres
• 7 Harmonic Analysis Associated to Reflection Groups
• 8 Boundedness of Projection Operator and Cesr̉o Means
• 9 Projection Operators and Cesr̉o Means in L^p Spaces
• 10 Weighted Best Approximation by Polynomials
• 11 Harmonic Analysis on the Unit Ball
• 12 Polynomial Approximation on the Unit Ball
• 13 Harmonic Analysis on the Simplex
• 14 Applications
• A Distance, Difference and Integral Formulas
• B Jacobi and Related Orthogonal Polynomials
• References
• Index
• Symbol Index.